Aspects of the disclosure relate to prosthetic valves having a frame, a frame cover, and a leaflet construct. Some aspects are directed to a diametric taper for the prosthetic valve for achieving enhanced performance of the prosthetic valve under operational conditions, enhanced compressibility and delivery characteristics, and other additional or alternative advantages. Other aspects are directed toward unique assembly and attachment methods for securing leaflet constructs to support structures. Other aspects are directed toward features for interacting with transcatheter delivery systems. Still other aspects are directed to such apparatuses, systems, and methods for valve replacement, such as cardiac valve replacement.